Krdytkyu

The following code

begin{tikzpicture}[scale=0.9]

begin{axis}[name=plot1, xlabel=clusters,colormap/blackwhite,legend style= 

{at={(0.95,0.95)}}]

addlegendimage{empty legend}

addlegendentry{Metrics}

addplot+[smooth]

coordinates{(2,21794) (3,11876) (4,7336) (5,5108) (6,3882) (7,2990)};

addlegendentry{a}

addplot+[smooth]

coordinates{(2,7.065608) (3,9.884279) (4,12.97898) (5,15.89754) (6,18.82487) 

(7,21.34288)};

addlegendentry{b}

end{axis}

end{tikzpicture}

produces the picture:

As we can see, the curves are very different in magnitude and so the trend of red curve seems to be constant. How can I draw these two curves with different scales?

This is not a complete answer. The following code just demonstrates how you can plot graphs in two different axes.

documentclass[border=3mm]{standalone}

usepackage{pgfplots}

begin{document}

begin{tikzpicture}[scale=0.9]

pgfplotsset{every axis legend/.style={

anchor= west,

draw=none,}

}



begin{axis}[name=plot1, xlabel=clusters,colormap/blackwhite,

y tick label style={blue},

legend style= {at={(0.78,0.55)}},

]

addplot[smooth,mark=*,blue]

coordinates{(2,21794) (3,11876) (4,7336) (5,5108) (6,3882) (7,2990)};

addlegendentry{a}

end{axis}



begin{axis}[name=plot2, axis y line*=right, axis x line=none,

 xlabel=clusters ,colormap/blackwhite, 

y tick label style={red},

legend style= {at={(0.78,0.45)}},

]

addplot[smooth,mark=square*,red]

coordinates{(2,7.065608) (3,9.884279) (4,12.97898) (5,15.89754) (6,18.82487) (7,21.34288)};

addlegendentry{b}

end{axis}

end{tikzpicture}

end{document}

You could use a semilogyaxis.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

begin{document}

begin{tikzpicture}[scale=0.9]

begin{semilogyaxis}[name=plot1, xlabel=clusters,colormap/blackwhite,legend style= 

{at={(0.95,0.6)}}]

addlegendimage{empty legend}

addlegendentry{Metrics}

addplot+[smooth]

coordinates{(2,21794) (3,11876) (4,7336) (5,5108) (6,3882) (7,2990)};

addlegendentry{a}

addplot+[smooth]

coordinates{(2,7.065608) (3,9.884279) (4,12.97898) (5,15.89754) (6,18.82487) 

(7,21.34288)};

addlegendentry{b}

end{semilogyaxis}

end{tikzpicture}

end{document}